Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C5 ⋊ #2056 |
288 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 288 conjugacy classes of subgroups — too many to draw. Only its 85 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 640 |
Polycyclic presentation:
2^7,5|a^2=g,b^2=g,c^2=d,d^2=g,e^2=g,f^2=g,b^a=bd,c^a=ce,d^a=dg,e^a=eg,f^a=fg,h^a=h^4,c^b=cf,d^b=dg,e^b=eg,f^b=fg,h^b=h^4,h^c=h^488 conjugacy classes — view the full character table.
| maximal subgroup of | #12011759, #12011764, #12011770, … |
| maximal normal subgroup of | #12011759, #12011764, #12011770, … |
| maximal quotient of | #12003135, #12003142, #12003163, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 1739);